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प्रश्न
Differentiate the following with respect to x.
sin(x2)
उत्तर
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
Let y = sin(x2)
`"dy"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
Here f = sin x, g = x2
`"dy"/"dx" = cos(x^2) "d"/"dx" (x^2)`
= cos(x2) (2x)
= 2x cos(x2)
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